Problem: If $x \otimes y = x^{2}+2y^{2}$ and $x \circledcirc y = x^{2}-4y^{2}$, find $(2 \circledcirc 1) \otimes 3$.
Answer: First, find $2 \circledcirc 1$ $ 2 \circledcirc 1 = 2^{2}-4(1^{2})$ $ \hphantom{2 \circledcirc 1} = 0$ Now, find $0 \otimes 3$ $ 0 \otimes 3 = 0^{2}+2(3^{2})$ $ \hphantom{0 \otimes 3} = 18$.